Aptitude Topics
Group Average
Techniques for tracking aggregate changes when sub-groups are added, removed, or mixed.
Fundamental Principles
Sub-Group Amalgamation
Analyzing distinct data compartments collectively to monitor structural effects on main group means.
Essential Formulation Tips
- Keep calculations minimal by analyzing balance shifts rather than multiplying large values directly.
Shortcut Execution Techniques
- When a person leaves and another joins: New Person = Replaced Person + (Change in Average * Total Count).
Contextual Inquiries (FAQs)
Q: Does swapping elements change item counts?
A: No, substitution models preserve the exact original dataset count size.
Example Breakdown: A Teacher Joins the Class
Extremely frequent competitive test variant.Problem QueryThe average age of 24 students is 15 years. If the teacher's age is included, the average increases by 1. Find the teacher's age.
Step-By-Step Solution Path
Previous count = 24. New count = 25.
New average = 15 + 1 = 16.
Teacher's age = (25 * 16) - (24 * 15) = 400 - 360 = 40 years.
Analytical Hint: Alternatively, evaluate using deviation: 15 + (1 * 25) = 40.
Group Substitution Problems
Test entries tracking dynamic roster variations.
Q1. 10 crew members weigh an average of 60 kg. One replaced member raises the average by 2 kg. If the old member was 50 kg, find the new one.